3 years ago

"If triangle vuw is equiangular, find k and t

Mathematics

1 answer:

balu736 [363]3 years ago

5 0

The answer is b. k=64 t=52.

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Determine the sum of the first 9 terms in the geometric series where r= -0.25 and a1= 256.

Damm [24]

$\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ r=-0.25\\ a_1=256\\ n=9 \end{cases}$

$\bf S_9=256\left(\cfrac{1-(-0.25)^9}{1-(-0.25)} \right)\implies S_9=256\left( \cfrac{1+0.25^9}{1+0.25} \right) \\\\\\ S_9=256\left( \cfrac{52429}{65536}\right)\implies S_9=\cfrac{52429}{256}\implies S_9=204.80078125$